Details

sample267.0ms

Algorithm

intervals

Results

87.0ms	56×	body	640	valid
79.0ms	97×	body	1280	valid
7.0ms	73×	body	80	valid
7.0ms	21×	body	320	valid
2.0ms	9×	body	160	valid

simplify36.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
1.9b	(cos (+ a b))

rewrite101.0ms

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))))
20.0ms	(/ (sin b) (cos (+ a b)))
38.0ms	(cos (+ a b))

series242.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(* r (/ (sin b) (cos (+ a b))))
80.0ms	(/ (sin b) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify5.2s

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

prune305.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (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))))

rewrite166.0ms

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:

32.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
84.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
17.0ms	(* (sin a) (sin b))
26.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series721.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
334.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
60.0ms	(* (sin a) (sin b))
213.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.3s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.2s)

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

prune574.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

18.0ms	(* r (sin b))
37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms	(* (sin a) (sin b))
33.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* r (sin b))
119.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(* (sin a) (sin b))
348.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.9s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	140	1256
1	345	1224
2	1091	1076
3	3874	989
done	5000	989

prune421.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
26.0ms	(* (sin a) (sin b))
53.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
90.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
55.0ms	(* (sin a) (sin b))
152.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
294.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify4.2s

Counts

122 → 122

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	181	2272
1	461	2088
2	1432	1834
3	4932	1768
done	5001	1768

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes241.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.2s	2947×	body	1280	valid
702.0ms	1827×	body	640	valid
204.0ms	756×	body	320	valid
174.0ms	2147×	body	80	valid
67.0ms	324×	body	160	valid