Details

sample373.0ms

Algorithm

intervals

Results

135.0ms	92×	body	1280	valid
114.0ms	53×	body	640	valid
39.0ms	72×	body	80	valid
10.0ms	25×	body	320	valid
4.0ms	15×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

47.0ms	(* r (/ (sin b) (cos (+ a b))))
20.0ms	(/ (sin b) (cos (+ a b)))
21.0ms	(cos (+ a b))

series193.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(* r (/ (sin b) (cos (+ a b))))
47.0ms	(/ (sin b) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify3.7s

Counts

82 → 82

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	659	834
3	1814	830
done	5001	824

prune401.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 113

Calls

4 calls:

12.0ms	(* (cos a) (cos b))
112.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms	(* (sin a) (sin b))
66.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos a) (cos b))
323.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
87.0ms	(* (sin a) (sin b))
212.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.7s

Counts

125 → 125

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	195	2025
1	442	1967
2	1261	1788
3	3587	1683
done	5000	1679

prune669.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`fma-neg`
6×	`pow1` `div-inv` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 128

Calls

4 calls:

31.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
11.0ms	(* (cos a) (cos b))
56.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
19.0ms	(/ (* (cos a) (cos b)) (sin b))

series576.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
61.0ms	(* (cos a) (cos b))
264.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
135.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.8s

Counts

140 → 140

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	216	2544
1	456	2233
2	1293	1954
done	5000	1825

prune773.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (cos b) (sin b))
0.2b	(fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a)))
0.2b	(/ r (fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`fma-udef`

Counts

3 → 68

Calls

3 calls:

16.0ms	(/ (cos b) (sin b))
1.0ms	(fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a)))
18.0ms	(/ r (fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a))))

series438.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ (cos b) (sin b))
150.0ms	(fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a)))
266.0ms	(/ r (fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a))))

simplify2.8s

Counts

77 → 77

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	138	1274
1	253	1141
2	571	1045
3	1297	1044
4	3331	1038
done	5000	1036

prune386.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes220.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	14	17
1	16	13
done	16	13

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.0s	2929×	body	1280	valid
1.5s	1872×	body	640	valid
738.0ms	2086×	body	80	valid
343.0ms	788×	body	320	valid
144.0ms	328×	body	160	valid