Details

sample48.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify23.0ms

Counts

1 → 1

Iterations

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

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize29.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
36.1b	(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))

series364.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
268.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify984.0ms

Counts

62 → 62

Iterations

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

prune481.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (fma y y (fma z z (* x x)))) (/ (sqrt (fma y y (fma z z (* x x)))) 3.0))
36.1b	(sqrt (fma y y (fma z z (* x x))))
36.1b	(sqrt (fma y y (fma z z (* x x))))
36.1b	(sqrt (* (sqrt (fma y y (fma z z (* x x)))) (/ (sqrt (fma y y (fma z z (* x x)))) 3.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
24×	`sqrt-prod`
22×	`times-frac` `associate-r`
21×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`cbrt-undiv` `sqrt-div` `div-exp` `*-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

25.0ms	(* (sqrt (fma y y (fma z z (* x x)))) (/ (sqrt (fma y y (fma z z (* x x)))) 3.0))
3.0ms	(sqrt (fma y y (fma z z (* x x))))
2.0ms	(sqrt (fma y y (fma z z (* x x))))
15.0ms	(sqrt (* (sqrt (fma y y (fma z z (* x x)))) (/ (sqrt (fma y y (fma z z (* x x)))) 3.0)))

series692.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sqrt (fma y y (fma z z (* x x)))) (/ (sqrt (fma y y (fma z z (* x x)))) 3.0))
153.0ms	(sqrt (fma y y (fma z z (* x x))))
204.0ms	(sqrt (fma y y (fma z z (* x x))))
251.0ms	(sqrt (* (sqrt (fma y y (fma z z (* x x)))) (/ (sqrt (fma y y (fma z z (* x x)))) 3.0)))

simplify2.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1889
1	270
0	117

prune677.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.3b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma z z (* x x))
0.1b	(* (fma y y (fma z z (* x x))) (/ 1 3.0))
36.1b	(sqrt (* (fma y y (fma z z (* x x))) (/ 1 3.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity` `add-exp-log`
11×	`times-frac` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube`
4×	`prod-exp`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`sqrt-pow1` `sqrt-div` `div-exp` `pow-prod-down` `associate-*r/` `un-div-inv` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `*-commutative` `sqrt-prod` `fma-udef` `div-inv`

Counts

3 → 63

Calls

3 calls:

0.0ms	(fma z z (* x x))
24.0ms	(* (fma y y (fma z z (* x x))) (/ 1 3.0))
12.0ms	(sqrt (* (fma y y (fma z z (* x x))) (/ 1 3.0)))

series447.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(fma z z (* x x))
110.0ms	(* (fma y y (fma z z (* x x))) (/ 1 3.0))
271.0ms	(sqrt (* (fma y y (fma z z (* x x))) (/ 1 3.0)))

simplify787.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1010
1	252
0	116

prune430.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.3b

localize24.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
36.1b	(sqrt (fma y y (fma x x (* z z))))

rewrite16.0ms

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:

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))))

series461.0ms

Counts

2 → 6

Calls

2 calls:

319.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
142.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify1.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
3	2046
2	463
1	161
0	104

prune395.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.0b

regimes878.0ms

Accuracy

42% (20.2b remaining)

Error of 26.2b against oracle of 6.0b and baseline of 40.8b

bsearch245.0ms

Steps

Iters	Range		Point
8	4.894347796388268e+59	1.6925211481097654e+62	9.098807375504896e+60
9	3.25461459604977e-148	1.0009102622850027e-138	3.4737339186177403e-147
8	-2.986264416976082e-65	-6.704894791063431e-68	-1.5953894216969175e-66
7	-7.317563595848081e+70	-3.854198347822332e+69	-6.500657693732615e+70
6	-3.1422350234624783e+87	-3.311258514422183e+86	-4.636290233423019e+86

simplify17.0ms

Iterations

Iter	Nodes
done	48
2	48
1	45
0	38

end0.0ms

sample1.0s

Algorithm

intervals

Results

645.0ms

8000×

body

valid