Details

sample29.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify59.0ms

Counts

1 → 1

Iterations

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

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize47.0ms

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))

rewrite31.0ms

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:

14.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
12.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series503.0ms

Counts

2 → 6

Calls

2 calls:

135.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
368.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify3.9s

Counts

64 → 64

Iterations

Iter	Nodes
done	5028
4	2302
3	728
2	321
1	169
0	103

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.5b

localize35.0ms

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:

10.0ms	(* (fma y y (fma z z (* x x))) 0.3333333333333333)
6.0ms	(sqrt (* (fma y y (fma z z (* x x))) 0.3333333333333333))

series460.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(* (fma y y (fma z z (* x x))) 0.3333333333333333)
346.0ms	(sqrt (* (fma y y (fma z z (* x x))) 0.3333333333333333))

simplify3.2s

Counts

41 → 41

Iterations

Iter	Nodes
done	5007
3	1226
2	307
1	124
0	62

prune611.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.0b

localize51.0ms

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))))

rewrite24.0ms

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:

15.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
3.0ms	(sqrt (fma y y (fma x x (* z z))))

series753.0ms

Counts

2 → 6

Calls

2 calls:

499.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
254.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify7.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5022
6	4189
5	2017
4	1102
3	492
2	271
1	163
0	106

prune971.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.8b

localize13.0ms

Local error

Found 1 expressions with local error:

0.1b	(* z (sqrt 0.3333333333333333))

rewrite26.0ms

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:

24.0ms

(* z (sqrt 0.3333333333333333))

series66.0ms

Counts

1 → 3

Calls

1 calls:

66.0ms

(* z (sqrt 0.3333333333333333))

simplify9.4s

Counts

28 → 28

Iterations

Iter	Nodes
done	5001
5	3236
4	1297
3	438
2	205
1	74
0	40

prune347.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 11.8b

regimes1.9s

Accuracy

47.8% (13.5b remaining)

Error of 25.7b against oracle of 12.2b and baseline of 38.1b

bsearch120.0ms

Steps

Iters	Range		Point
5	3.974905491533812e+107	1.4840184546072852e+108	6.10812431813731e+107
8	-3.2381721935150553e+97	-1.6115880045118348e+94	-3.1284007528331483e+97

simplify7.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.6s

8000×

body

valid