Details

sample28.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize40.0ms

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

series420.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(fma x x (* z z))
95.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
266.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify2.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	5002
4	3349
3	925
2	366
1	182
0	115

prune505.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.2b

localize32.0ms

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))))

rewrite34.0ms

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:

3.0ms	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
19.0ms	(* (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 1)) (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))
2.0ms	(sqrt (fma y y (fma x x (* z z))))
3.0ms	(sqrt (fma y y (fma x x (* z z))))

series886.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
282.0ms	(* (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 1)) (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))
169.0ms	(sqrt (fma y y (fma x x (* z z))))
189.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify2.5s

Counts

176 → 176

Iterations

Iter	Nodes
done	5001
3	2503
2	802
1	348
0	210

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.2b

localize45.0ms

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)))
37.1b	(sqrt (fma y y (fma x x (* z z))))

rewrite29.0ms

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` `insert-posit16` `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 → 75

Calls

3 calls:

0.0ms	(fma x x (* z z))
24.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
2.0ms	(sqrt (fma y y (fma x x (* z z))))

series515.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma x x (* z z))
238.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
215.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify2.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	2769
3	887
2	421
1	198
0	115

prune409.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.2b

localize6.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

7.0ms

(* z (sqrt 0.3333333333333333))

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

(* z (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

prune63.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 19.2b

regimes273.0ms

Accuracy

64.5% (6.2b remaining)

Error of 24.3b against oracle of 18.1b and baseline of 35.7b

bsearch71.0ms

Steps

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

simplify5.0ms

Iterations

Iter	Nodes
done	26
2	26
1	23
0	20

end0.0ms

sample686.0ms

Algorithm

intervals

Results

531.0ms

8000×

body

valid