Details

sample228.0ms

Algorithm

intervals

Results

116.0ms	104×	body	1280	valid
25.0ms	50×	body	640	valid
8.0ms	29×	body	320	valid
5.0ms	62×	body	80	valid
3.0ms	11×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

localize15.0ms

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))

rewrite59.0ms

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×	`associate-l` `associate-/r` `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 → 67

Calls

3 calls:

31.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
13.0ms	(cos (+ a b))

series195.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(* r (/ (sin b) (cos (+ a b))))
42.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify5.1s

Counts

76 → 76

Iterations

Useful iterations: 4 (3.6s)

Iter	Nodes	Cost
0	116	909
1	249	883
2	638	793
3	1727	785
4	4912	783
done	5000	783

prune330.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))))

rewrite207.0ms

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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
136.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
14.0ms	(* (sin a) (sin b))
32.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
317.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
87.0ms	(* (sin a) (sin b))
186.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.5s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1162	1856
3	3369	1715
done	5001	1715

prune590.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`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` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

12.0ms	(* (cos a) (cos b))
34.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
42.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
28.0ms	(/ (* (cos a) (cos b)) (sin b))

series584.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (cos a) (cos b))
140.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
283.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
109.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify3.0s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1052	1436
3	4003	1430
done	5000	1430

prune673.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
4.5b	(log (exp (* (sin a) (sin b))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`log-prod` `prod-exp` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `rem-log-exp` `clear-num` `sin-mult`

Counts

4 → 96

Calls

4 calls:

97.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
29.0ms	(* (sin a) (sin b))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
8.0ms	(log (exp (* (sin a) (sin b))))

series670.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
67.0ms	(* (sin a) (sin b))
187.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
73.0ms	(log (exp (* (sin a) (sin b))))

simplify2.8s

Counts

108 → 108

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	164	1992
1	355	1744
2	988	1576
3	2781	1507
done	5001	1507

prune632.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes246.0ms

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: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	17	18
done	17	18

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.2s	2904×	body	1280	valid
1.5s	1843×	body	640	valid
312.0ms	770×	body	320	valid
285.0ms	2146×	body	80	valid
80.0ms	339×	body	160	valid