Details

sample372.0ms

Algorithm

intervals

Results

116.0ms	92×	body	1280	valid
112.0ms	53×	body	640	valid
12.0ms	72×	body	80	valid
10.0ms	25×	body	320	valid
5.0ms	15×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 15.8b

localize30.0ms

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))

rewrite69.0ms

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:

37.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
16.0ms	(cos (+ a b))

series290.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(* r (/ (sin b) (cos (+ a b))))
66.0ms	(/ (sin b) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify6.0s

Counts

76 → 76

Iterations

Useful iterations: 4 (4.4s)

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

prune303.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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))))

rewrite209.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 105

Calls

4 calls:

15.0ms	(* (cos a) (cos b))
94.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms	(* (sin a) (sin b))
56.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series685.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (cos a) (cos b))
356.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
78.0ms	(* (sin a) (sin b))
199.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.7s

Counts

117 → 117

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	187	1937
1	425	1883
2	1214	1707
3	3353	1606
done	5000	1606

prune624.0ms

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))

rewrite128.0ms

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:

29.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
12.0ms	(* (cos a) (cos b))
68.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
15.0ms	(/ (* (cos a) (cos b)) (sin b))

series616.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
54.0ms	(* (cos a) (cos b))
302.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
116.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify3.2s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1051	1436
3	4001	1430
done	5000	1430

prune503.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.2b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `flip--` `div-inv` `sub-div` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 114

Calls

4 calls:

16.0ms	(* r (sin b))
65.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))
100.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* r (sin b))
156.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
58.0ms	(* (sin a) (sin b))
363.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify4.4s

Counts

126 → 126

Iterations

Useful iterations: 3 (2.6s)

Iter	Nodes	Cost
0	182	2093
1	451	1915
2	1373	1669
3	4597	1621
done	5000	1621

prune522.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes245.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	12	13
done	12	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.9s	2929×	body	1280	valid
1.3s	1872×	body	640	valid
440.0ms	2086×	body	80	valid
300.0ms	788×	body	320	valid
75.0ms	328×	body	160	valid