Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize26.0ms

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)
32.8b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite10.0ms

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

series384.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma x x (* z z))
112.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
211.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify1.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5002
3	2089
2	514
1	179
0	112

prune513.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* z z))
0.1b	(* 0.3333333333333333 (fma y y (fma x x (* z z))))
32.8b	(sqrt (* 0.3333333333333333 (fma y y (fma x x (* z z)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

0.0ms	(fma x x (* z z))
6.0ms	(* 0.3333333333333333 (fma y y (fma x x (* z z))))
6.0ms	(sqrt (* 0.3333333333333333 (fma y y (fma x x (* z z)))))

series395.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(fma x x (* z z))
94.0ms	(* 0.3333333333333333 (fma y y (fma x x (* z z))))
235.0ms	(sqrt (* 0.3333333333333333 (fma y y (fma x x (* z z)))))

simplify1.8s

Counts

54 → 54

Iterations

Iter	Nodes
done	5002
3	3445
2	614
1	149
0	76

prune301.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.2b

localize21.0ms

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 3.0))
32.7b	(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))
13.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
2.0ms	(sqrt (fma y y (fma x x (* z z))))

series545.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma x x (* z z))
313.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
171.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2325
2	540
1	180
0	117

prune490.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (sqrt 0.3333333333333333))

rewrite9.0ms

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

(* y (sqrt 0.3333333333333333))

series65.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

(* y (sqrt 0.3333333333333333))

simplify2.5s

Counts

27 → 27

Iterations

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

prune100.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 16.1b

regimes483.0ms

Accuracy

63.4% (7.4b remaining)

Error of 25.5b against oracle of 18.1b and baseline of 38.3b

bsearch121.0ms

Steps

Iters	Range		Point
9	7.325601126918715e+111	1.1343483352271129e+117	6.557174003264764e+116
10	-1.1071683335692419e+166	-3.0632372757179626e+150	-2.942680527553483e+151

simplify4.0ms

Iterations

Iter	Nodes
done	26
2	26
1	24
0	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

816.0ms

8000×

body

valid