Details

sample27.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	20
1	13
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
5×	`add-sqr-sqrt`
4×	`pow1` `sum-log` `*-un-lft-identity` `add-cube-cbrt`
3×	`flip3-+` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `flip-+`
2×	`+-commutative` `sqrt-div`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

3 → 39

Calls

3 calls:

24.0ms	(+ (+ (* x x) (* y y)) (* z z))
6.0ms	(+ (* x x) (* y y))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (+ (* x x) (* y y)) (* z z))
34.0ms	(+ (* x x) (* y y))
110.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify834.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1301
1	236
0	74

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.5b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

9.0ms	(+ (* x x) (* y y))
161.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
36.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x x) (* y y))
119.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
119.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
118.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.5s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1707
1	345
0	137

prune579.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* z z) (* y y)) (* x x))
0.1b	(* (+ (+ (* z z) (* y y)) (* x x)) (sqrt (+ (+ (* z z) (* y y)) (* x x))))
36.1b	(sqrt (+ (+ (* z z) (* y y)) (* x x)))
44.0b	(cbrt (* (+ (+ (* z z) (* y y)) (* x x)) (sqrt (+ (+ (* z z) (* y y)) (* x x)))))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`flip3-+` `sqrt-div` `flip-+`
10×	`pow1`
9×	`add-log-exp`
8×	`frac-times` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-prod`
6×	`add-cbrt-cube` `associate-r` `add-exp-log`
4×	`associate-l/` `associate-r/`
3×	`sum-log` `associate-l`
2×	`sqrt-pow1` `pow1/2` `pow3` `pow-prod-up` `unswap-sqr`
1×	`cbrt-prod` `+-commutative` `rem-sqrt-square` `associate-+l+` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

24.0ms	(+ (+ (* z z) (* y y)) (* x x))
145.0ms	(* (+ (+ (* z z) (* y y)) (* x x)) (sqrt (+ (+ (* z z) (* y y)) (* x x))))
37.0ms	(sqrt (+ (+ (* z z) (* y y)) (* x x)))
51.0ms	(cbrt (* (+ (+ (* z z) (* y y)) (* x x)) (sqrt (+ (+ (* z z) (* y y)) (* x x)))))

series615.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (+ (* z z) (* y y)) (* x x))
296.0ms	(* (+ (+ (* z z) (* y y)) (* x x)) (sqrt (+ (+ (* z z) (* y y)) (* x x))))
110.0ms	(sqrt (+ (+ (* z z) (* y y)) (* x x)))
155.0ms	(cbrt (* (+ (+ (* z z) (* y y)) (* x x)) (sqrt (+ (+ (* z z) (* y y)) (* x x)))))

simplify1.3s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1536
1	291
0	125

prune555.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 13.6b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 13.6b

regimes880.0ms

Accuracy

45.7% (13.5b remaining)

Error of 25.8b against oracle of 12.2b and baseline of 37.1b

bsearch75.0ms

Steps

Iters	Range		Point
9	1.5958334848383986e+119	1.6343128467780486e+124	7.898403675517638e+123
9	-7.123290046831777e+50	-4.989343308395731e+45	-7.0606062487436015e+50

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample786.0ms

Algorithm

intervals

Results

465.0ms

8000×

body

valid