Details

sample18.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
3	20
2	19
1	13
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize15.0ms

Local error

Found 1 expressions with local error:

35.7b

(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

1 → 16

Calls

1 calls:

37.0ms

(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series156.0ms

Counts

1 → 3

Calls

1 calls:

155.0ms

(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.8s

Counts

19 → 19

Iterations

Iter	Nodes
done	5004
4	3296
3	922
2	266
1	93
0	42

prune120.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.3b

localize48.0ms

Local error

Found 4 expressions with local error:

19.1b	(sqrt (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
36.9b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
36.9b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
36.9b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 70

Calls

4 calls:

46.0ms	(sqrt (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
28.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
26.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
24.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(sqrt (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
141.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
137.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
115.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.3s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
3	1723
2	494
1	205
0	105

prune480.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.3b

localize24.0ms

Local error

Found 2 expressions with local error:

6.1b	(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`log-prod` `exp-prod` `*-un-lft-identity` `exp-sum` `add-cube-cbrt` `sqrt-prod`
5×	`pow1`
4×	`sqrt-div`
3×	`log-pow`
2×	`log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `exp-diff` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

2 → 39

Calls

2 calls:

25.0ms	(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
44.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series289.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
153.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.0s

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
4	2799
3	922
2	322
1	143
0	82

prune252.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.3b

localize53.0ms

Local error

Found 4 expressions with local error:

6.0b	(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow-unpow` `sqrt-prod`
6×	`cbrt-prod` `sqrt-div`
5×	`add-log-exp`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `unpow-prod-down` `pow-pow` `flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

9.0ms	(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
30.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series844.0ms

Counts

4 → 12

Calls

4 calls:

463.0ms	(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
143.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
128.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
110.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	1841
2	587
1	218
0	91

prune491.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.3b

regimes701.0ms

Accuracy

64.9% (6.1b remaining)

Error of 23.4b against oracle of 17.3b and baseline of 34.7b

bsearch76.0ms

Steps

Iters	Range		Point
10	2.529877801601859e+142	4.190548468910152e+156	1.3381067656623604e+154
9	-1.712097807796962e+159	-9.907787135739815e+151	-1.048501675377615e+153

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample795.0ms

Algorithm

intervals

Results

595.0ms

8000×

body

valid