Details

sample21.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	22
3	22
2	21
1	15
0	11

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`sum-log` `insert-posit16`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp`

Counts

4 → 82

Calls

4 calls:

15.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (* x x) (* y y)) (* z z))
90.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
54.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series391.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x x) (* y y))
48.0ms	(+ (+ (* x x) (* y y)) (* z z))
85.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
221.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1048
1	337
0	143

prune614.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
32.9b	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
51×	`times-frac` `add-exp-log`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
24×	`cbrt-prod`
22×	`associate-r`
20×	`prod-exp`
19×	`add-cbrt-cube`
16×	`div-exp`
9×	`pow1` `add-log-exp` `unswap-sqr`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
4×	`rec-exp` `1-exp` `insert-posit16`
3×	`sum-log` `sqrt-div` `div-inv` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+` `clear-num` `frac-2neg` `pow1/2` `*-commutative` `sqrt-prod`

Counts

4 → 142

Calls

4 calls:

50.0ms	(+ (+ (* x x) (* y y)) (* z z))
139.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
88.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
41.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

series950.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (+ (* x x) (* y y)) (* z z))
211.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
216.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
465.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

simplify2.1s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	2464
1	680
0	227

prune823.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`sqrt-prod`
17×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-log-exp`
9×	`pow1` `sqrt-div`
8×	`unswap-sqr`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`sum-log` `insert-posit16`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `+-commutative` `associate-*l/`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-unprod` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 92

Calls

4 calls:

9.0ms	(+ (* x x) (* y y))
37.0ms	(+ (+ (* x x) (* y y)) (* z z))
80.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
25.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x x) (* y y))
42.0ms	(+ (+ (* x x) (* y y)) (* z z))
209.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
118.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5011
3	4926
2	1010
1	364
0	155

prune511.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (* z z))
0.0b	(+ (+ (* y y) (* z z)) (* x x))
0.4b	(/ (sqrt (+ (+ (* y y) (* z z)) (* x x))) (sqrt 3.0))
32.8b	(sqrt (+ (+ (* y y) (* z z)) (* x x)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-log-exp`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`sum-log` `flip3-+` `sqrt-div` `flip-+` `insert-posit16`
2×	`+-commutative` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 106

Calls

4 calls:

15.0ms	(+ (* y y) (* z z))
37.0ms	(+ (+ (* y y) (* z z)) (* x x))
65.0ms	(/ (sqrt (+ (+ (* y y) (* z z)) (* x x))) (sqrt 3.0))
26.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* y y) (* z z))
58.0ms	(+ (+ (* y y) (* z z)) (* x x))
315.0ms	(/ (sqrt (+ (+ (* y y) (* z z)) (* x x))) (sqrt 3.0))
151.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))

simplify1.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	5008
2	1101
1	350
0	156

prune502.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.0b

regimes823.0ms

Accuracy

38.1% (17.5b remaining)

Error of 24.1b against oracle of 6.6b and baseline of 34.8b

bsearch99.0ms

Steps

Iters	Range		Point
8	5.505283103902098e+120	2.9276084226034184e+124	2.8767154662268737e+124
8	-4.448318838164251e+147	-1.2024808101929759e+144	-1.9223608795668832e+146

simplify8.0ms

Iterations

Iter	Nodes
done	38
2	38
1	35
0	27

end0.0ms

sample989.0ms

Algorithm

intervals

Results

832.0ms

8000×

body

valid