Details

sample35.0ms

Algorithm

intervals

Results

19.0ms

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: 36.2b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* z z))
0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
33.6b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite18.0ms

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` `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 → 66

Calls

3 calls:

0.0ms	(fma x x (* z z))
7.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
6.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series396.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma x x (* z z))
86.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
246.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify2.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5009
4	3536
3	916
2	360
1	179
0	112

prune483.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* z z))
0.3b	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
33.6b	(sqrt (fma y y (fma x x (* z z))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r` `associate-/l`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`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` `fma-udef` `div-inv`

Counts

3 → 88

Calls

3 calls:

0.0ms	(fma x x (* z z))
11.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
3.0ms	(sqrt (fma y y (fma x x (* z z))))

series473.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma x x (* z z))
287.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
140.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify2.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5003
4	2121
3	738
2	338
1	180
0	117

prune526.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.9b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* z z))
0.4b	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
33.6b	(sqrt (fma y y (fma x x (* z z))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `sqrt-div` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 72

Calls

3 calls:

0.0ms	(fma x x (* z z))
23.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
3.0ms	(sqrt (fma y y (fma x x (* z z))))

series827.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(fma x x (* z z))
268.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
501.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify2.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5040
4	2618
3	859
2	410
1	195
0	112

prune366.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.9b

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(* z (sqrt 0.3333333333333333))

rewrite8.0ms

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:

8.0ms

(* z (sqrt 0.3333333333333333))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(* z (sqrt 0.3333333333333333))

simplify4.7s

Counts

27 → 27

Iterations

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

prune69.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 16.9b

regimes458.0ms

Accuracy

63.3% (7.1b remaining)

Error of 25.3b against oracle of 18.2b and baseline of 37.5b

bsearch110.0ms

Steps

Iters	Range		Point
10	1.4223746807816657e+94	4.650036525585027e+111	4.5816600794380617e+111
8	-1.9107382794363858e+145	-5.055601083106867e+141	-7.465878436556341e+142

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample814.0ms

Algorithm

intervals

Results

570.0ms

8000×

body

valid