Details

sample208.0ms

Algorithm

intervals

Results

102.0ms	104×	body	1280	valid
18.0ms	50×	body	640	valid
7.0ms	29×	body	320	valid
4.0ms	62×	body	80	valid
2.0ms	11×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite85.0ms

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:

56.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
12.0ms	(cos (+ a b))

series240.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(* r (/ (sin b) (cos (+ a b))))
45.0ms	(/ (sin b) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify3.6s

Counts

82 → 82

Iterations

Useful iterations: done (3.6s)

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

prune313.0ms

Pruning

11 alts after pruning (11 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))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
141.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms	(* (sin a) (sin b))
57.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series802.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
375.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
58.0ms	(* (sin a) (sin b))
217.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.8s

Counts

122 → 122

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1244	1949
3	3754	1826
done	5000	1821

prune737.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

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:

11.0ms	(* (cos a) (cos b))
40.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
69.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
28.0ms	(/ (* (cos a) (cos b)) (sin b))

series644.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cos a) (cos b))
122.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
307.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
145.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.7s

Counts

140 → 140

Iterations

Useful iterations: done (1.7s)

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

prune759.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

384×	`times-frac`
295×	`add-sqr-sqrt`
260×	`*-un-lft-identity`
250×	`add-cube-cbrt`
132×	`prod-diff`
44×	`fma-neg`
23×	`associate-/r*` `div-inv`
15×	`difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`associate-/r/`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 342

Calls

4 calls:

114.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
18.0ms	(/ (sin b) (cos a))
110.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
38.0ms	(/ (cos b) (/ (sin b) (cos a)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
80.0ms	(/ (sin b) (cos a))
261.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
117.0ms	(/ (cos b) (/ (sin b) (cos a)))

simplify1.9s

Counts

354 → 354

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	434	9253
1	915	7401
2	2459	6502
done	5001	5787

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
done	11	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.4s	2904×	body	1280	valid
1.1s	1843×	body	640	valid
286.0ms	770×	body	320	valid
253.0ms	2146×	body	80	valid
74.0ms	339×	body	160	valid