Details

sample177.0ms

Algorithm

intervals

Results

54.0ms	64×	body	1280	valid
34.0ms	249×	body	80	valid
33.0ms	54×	body	640	valid
27.0ms	13×	body	160	valid
11.0ms	27×	body	320	valid

simplify100.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
0.4b	(/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
95×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
27×	`associate-/r*`
11×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`flip3-+` `flip-+` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `insert-posit16`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

3 → 169

Calls

3 calls:

8.0ms	(+ (* a1 a1) (* a2 a2))
21.0ms	(/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
16.0ms	(/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))

series418.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* a1 a1) (* a2 a2))
282.0ms	(/ (cos th) (/ (sqrt 2) (+ (* a1 a1) (* a2 a2))))
91.0ms	(/ (sqrt 2) (+ (* a1 a1) (* a2 a2)))

simplify1.7s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	2124
1	661
0	256

prune931.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (* a2 a2) (* a1 a1))) (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (sqrt 2)))
0.4b	(/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (sqrt 2))
7.8b	(sqrt (+ (* a2 a2) (* a1 a1)))
7.8b	(sqrt (+ (* a2 a2) (* a1 a1)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`sqrt-div` `associate-r`
8×	`pow1`
6×	`associate-/r` `associate-l*`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-*r/`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `div-inv` `unswap-sqr` `associate-/l/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 101

Calls

4 calls:

79.0ms	(* (sqrt (+ (* a2 a2) (* a1 a1))) (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (sqrt 2)))
34.0ms	(/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (sqrt 2))
13.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
13.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (sqrt (+ (* a2 a2) (* a1 a1))) (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (sqrt 2)))
298.0ms	(/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (sqrt 2))
58.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
65.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))

simplify3.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5004
3	4911
2	1174
1	374
0	143

prune743.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (* a2 a2) (* a1 a1))) (/ (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))))
0.3b	(/ (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
7.8b	(sqrt (+ (* a2 a2) (* a1 a1)))
7.8b	(sqrt (+ (* a2 a2) (* a1 a1)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
85×	`add-sqr-sqrt`
70×	`cbrt-prod`
61×	`*-un-lft-identity` `add-cube-cbrt`
49×	`associate-r`
48×	`sqrt-prod`
47×	`add-exp-log`
29×	`add-cbrt-cube`
21×	`div-inv`
18×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
9×	`associate-/r*`
8×	`pow1` `sqrt-div` `unswap-sqr`
6×	`associate-l`
5×	`associate-/l*`
4×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 203

Calls

4 calls:

84.0ms	(* (sqrt (+ (* a2 a2) (* a1 a1))) (/ (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))))
38.0ms	(/ (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
6.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
6.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(* (sqrt (+ (* a2 a2) (* a1 a1))) (/ (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))))
237.0ms	(/ (/ (* (cos th) (sqrt (+ (* a2 a2) (* a1 a1)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
52.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
61.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))

simplify2.2s

Counts

215 → 215

Iterations

Iter	Nodes
done	5084
2	2659
1	765
0	278

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (+ (* a1 a1) (* a2 a2)) (cos th))
0.4b	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac` `sqrt-prod`
5×	`pow1` `add-log-exp`
4×	`associate-*l/`
3×	`flip3-+` `associate-r` `associate-l` `flip-+` `insert-posit16`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

15.0ms	(+ (* a1 a1) (* a2 a2))
43.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
31.0ms	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2))

series409.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (* a1 a1) (* a2 a2))
141.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
233.0ms	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2))

simplify2.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	4100
2	899
1	289
0	114

prune321.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes307.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.8s	2488×	body	1280	valid
2.3s	2069×	body	640	valid
1.5s	7948×	body	80	valid
650.0ms	1037×	body	320	valid
183.0ms	511×	body	160	valid