Details

sample31.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	25
3	25
2	22
1	15
0	11

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (+ (* x x) (* z z)))
0.0b	(+ (* x x) (* z z))
0.1b	(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
32.8b	(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

rewrite124.0ms

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`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+r+` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp`

Counts

4 → 78

Calls

4 calls:

16.0ms	(+ (* y y) (+ (* x x) (* z z)))
9.0ms	(+ (* x x) (* z z))
75.0ms	(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
22.0ms	(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

series389.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* y y) (+ (* x x) (* z z)))
41.0ms	(+ (* x x) (* z z))
68.0ms	(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
220.0ms	(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

simplify996.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	2059
1	373
0	138

prune700.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (+ (* x x) (* z z)))
0.0b	(+ (* x x) (* z z))
0.2b	(* (+ (* y y) (+ (* x x) (* z z))) (/ 1 3.0))
32.8b	(sqrt (* (+ (* y y) (+ (* x x) (* z z))) (/ 1 3.0)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*` `add-exp-log`
12×	`add-cube-cbrt`
11×	`times-frac` `add-log-exp`
9×	`pow1` `add-cbrt-cube`
6×	`flip3-+` `sqrt-div` `flip-+`
4×	`frac-times` `sum-log` `associate-*l/` `prod-exp`
3×	`associate-l` `unswap-sqr`
2×	`+-commutative` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-*r/` `un-div-inv` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `associate-+r+` `pow1/2` `1-exp` `*-commutative` `sqrt-prod` `div-inv`

Counts

4 → 81

Calls

4 calls:

28.0ms	(+ (* y y) (+ (* x x) (* z z)))
12.0ms	(+ (* x x) (* z z))
107.0ms	(* (+ (* y y) (+ (* x x) (* z z))) (/ 1 3.0))
39.0ms	(sqrt (* (+ (* y y) (+ (* x x) (* z z))) (/ 1 3.0)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* y y) (+ (* x x) (* z z)))
38.0ms	(+ (* x x) (* z z))
86.0ms	(* (+ (* y y) (+ (* x x) (* z z))) (/ 1 3.0))
254.0ms	(sqrt (* (+ (* y y) (+ (* x x) (* z z))) (/ 1 3.0)))

simplify3.4s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	3659
1	463
0	155

prune554.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.2b

localize21.0ms

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))
32.7b	(sqrt (+ (+ (* y y) (* z z)) (* x x)))

rewrite166.0ms

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-+`
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 → 102

Calls

4 calls:

6.0ms	(+ (* y y) (* z z))
42.0ms	(+ (+ (* y y) (* z z)) (* x x))
83.0ms	(/ (sqrt (+ (+ (* y y) (* z z)) (* x x))) (sqrt 3.0))
32.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* y y) (* z z))
57.0ms	(+ (+ (* y y) (* z z)) (* x x))
333.0ms	(/ (sqrt (+ (+ (* y y) (* z z)) (* x x))) (sqrt 3.0))
151.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))

simplify920.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	2128
1	371
0	152

prune553.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* (sqrt 0.3333333333333333) y)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-l`
4×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
3×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

8.0ms

(* (sqrt 0.3333333333333333) y)

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(* (sqrt 0.3333333333333333) y)

simplify1.0s

Counts

25 → 25

Iterations

Iter	Nodes
done	5001
3	1495
2	255
1	70
0	35

prune102.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.0b

regimes1.0s

Accuracy

48.9% (13.4b remaining)

Error of 25.5b against oracle of 12.1b and baseline of 38.3b

bsearch96.0ms

Steps

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

simplify11.0ms

Iterations

Iter	Nodes
done	35
2	35
1	32
0	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

728.0ms

8000×

body

valid