Details

sample342.0ms

Algorithm

intervals

Results

85.0ms	100×	body	1280	valid
83.0ms	54×	body	640	valid
38.0ms	67×	body	80	valid
11.0ms	28×	body	320	valid
2.0ms	7×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite87.0ms

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:

48.0ms	(* r (/ (sin b) (cos (+ a b))))
19.0ms	(/ (sin b) (cos (+ a b)))
17.0ms	(cos (+ a b))

series247.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(* r (/ (sin b) (cos (+ a b))))
68.0ms	(/ (sin b) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify2.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5004
3	3136
2	844
1	271
0	120

prune483.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
143.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(* (sin a) (sin b))
31.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
330.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
66.0ms	(* (sin a) (sin b))
147.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1468
1	439
0	175

prune899.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms	(* (sin b) r)
11.0ms	(* (sin a) (sin b))
33.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms	(* (sin b) r)
77.0ms	(* (sin a) (sin b))
331.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
3	4912
2	1199
1	367
0	144

prune549.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
0.1b	(/ (sin b) (cos a))
0.2b	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
0.3b	(/ (cos b) (/ (sin b) (cos a)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
111×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
66×	`add-cube-cbrt`
23×	`associate-/r*`
15×	`difference-of-squares`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 162

Calls

4 calls:

47.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
15.0ms	(/ (sin b) (cos a))
49.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
11.0ms	(/ (cos b) (/ (sin b) (cos a)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
82.0ms	(/ (sin b) (cos a))
289.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
92.0ms	(/ (cos b) (/ (sin b) (cos a)))

simplify1.6s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	1909
1	643
0	285

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes249.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.5s	2928×	body	1280	valid
1.1s	1854×	body	640	valid
389.0ms	787×	body	320	valid
269.0ms	2083×	body	80	valid
94.0ms	352×	body	160	valid