Details

sample351.0ms

Algorithm

intervals

Results

130.0ms	95×	body	1280	valid
33.0ms	48×	body	640	valid
16.0ms	27×	body	320	valid
14.0ms	68×	body	80	valid
6.0ms	18×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
4	21
3	20
2	16
1	12
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 70

Calls

3 calls:

14.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
30.0ms	(cos (+ a b))

series183.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(* r (/ (sin b) (cos (+ a b))))
48.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify827.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	1058
1	276
0	120

prune470.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 109

Calls

4 calls:

9.0ms	(* (cos a) (cos b))
98.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
19.0ms	(* (sin a) (sin b))
48.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (cos a) (cos b))
374.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
64.0ms	(* (sin a) (sin b))
149.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2043
1	470
0	192

prune850.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* (sin b) r)
0.2b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 85

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
14.0ms	(* (sin b) r)
33.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
11.0ms	(* (sin b) (sin a))

series506.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (cos a) (cos b))
44.0ms	(* (sin b) r)
319.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
66.0ms	(* (sin b) (sin a))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1942
1	390
0	164

prune627.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 109

Calls

4 calls:

9.0ms	(* (cos a) (cos b))
40.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
21.0ms	(* (sin b) (sin a))
125.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos a) (cos b))
261.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
51.0ms	(* (sin b) (sin a))
334.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

simplify1.7s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2296
1	472
0	196

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes246.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.9s	2918×	body	1280	valid
1.7s	1912×	body	640	valid
745.0ms	2095×	body	80	valid
397.0ms	705×	body	320	valid
124.0ms	370×	body	160	valid