Details

sample43.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify11.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
35.3b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite17.0ms

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:

8.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
7.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series345.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
256.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	1755
2	455
1	167
0	101

prune451.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma z z (* x x))
0.4b	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
35.2b	(sqrt (fma y y (fma z z (* x x))))

rewrite11.0ms

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 z z (* x x))
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))))

series636.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(fma z z (* x x))
370.0ms	(/ (sqrt (fma y y (fma z z (* x x)))) (sqrt 3.0))
197.0ms	(sqrt (fma y y (fma z z (* x x))))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2314
2	539
1	179
0	117

prune491.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.9b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma z z (* x x))
0.4b	(* (sqrt (fma y y (fma z z (* x x)))) (sqrt (/ 1 3.0)))
35.2b	(sqrt (fma y y (fma z z (* x x))))

rewrite23.0ms

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

series538.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma z z (* x x))
241.0ms	(* (sqrt (fma y y (fma z z (* x x)))) (sqrt (/ 1 3.0)))
249.0ms	(sqrt (fma y y (fma z z (* x x))))

simplify2.8s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
3	3744
2	600
1	194
0	112

prune548.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 9.9b

localize9.0ms

Local error

Found 1 expressions with local error:

0.2b	(* z (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` `log1p-expm1-u` `add-log-exp`

Counts

1 → 24

Calls

1 calls:

15.0ms

(* z (sqrt 0.3333333333333333))

series78.0ms

Counts

1 → 3

Calls

1 calls:

78.0ms

(* z (sqrt 0.3333333333333333))

simplify2.8s

Counts

27 → 27

Iterations

Iter	Nodes
done	5001
5	4301
4	2012
3	712
2	201
1	75
0	39

prune84.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 9.9b

regimes979.0ms

Accuracy

47.7% (13.4b remaining)

Error of 26.0b against oracle of 12.6b and baseline of 38.1b

bsearch122.0ms

Steps

Iters	Range		Point
6	2.6913520219809045e+92	3.9657822087457923e+93	3.9027316219453185e+93
8	-5.250355123902004e+120	-1.540786475003901e+118	-8.482917924797484e+119

simplify13.0ms

Iterations

Iter	Nodes
done	32
3	32
2	31
1	27
0	22

end0.0ms

sample1.2s

Algorithm

intervals

Results

753.0ms

8000×

body

valid