Details

sample341.0ms

Algorithm

intervals

Results

78.0ms	95×	body	1280	valid
23.0ms	48×	body	640	valid
11.0ms	68×	body	80	valid
10.0ms	27×	body	320	valid
4.0ms	18×	body	160	valid

simplify384.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize121.0ms

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))

rewrite103.0ms

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:

43.0ms	(* r (/ (sin b) (cos (+ a b))))
25.0ms	(/ (sin b) (cos (+ a b)))
29.0ms	(cos (+ a b))

series322.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(* r (/ (sin b) (cos (+ a b))))
83.0ms	(/ (sin b) (cos (+ a b)))
43.0ms	(cos (+ a b))

simplify5.6s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	3110
2	844
1	272
0	120

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize171.0ms

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))))

rewrite453.0ms

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:

45.0ms	(* (cos a) (cos b))
265.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
45.0ms	(* (sin a) (sin b))
84.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.2s

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (cos a) (cos b))
695.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
106.0ms	(* (sin a) (sin b))
330.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.9s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	1513
1	466
0	192

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize129.0ms

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 a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite221.0ms

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:

38.0ms	(* (cos a) (cos b))
46.0ms	(* (sin b) r)
89.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))

series950.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (cos a) (cos b))
74.0ms	(* (sin b) r)
663.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms	(* (sin a) (sin b))

simplify3.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5004
2	1258
1	393
0	161

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize150.0ms

Local error

Found 4 expressions with local error:

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

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `div-inv` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 96

Calls

4 calls:

78.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
32.0ms	(* (cos b) (cos a))
38.0ms	(/ (* (cos b) (cos a)) (sin b))
79.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series1.0s

Counts

4 → 12

Calls

4 calls:

224.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
118.0ms	(* (cos b) (cos a))
151.0ms	(/ (* (cos b) (cos a)) (sin b))
531.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify8.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	5013
3	4629
2	1128
1	390
0	179

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes844.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.5s	2918×	body	1280	valid
1.6s	1912×	body	640	valid
382.0ms	705×	body	320	valid
359.0ms	2095×	body	80	valid
141.0ms	370×	body	160	valid