Details

sample347.0ms

Algorithm

intervals

Results

107.0ms	95×	body	1280	valid
64.0ms	68×	body	80	valid
35.0ms	48×	body	640	valid
14.0ms	27×	body	320	valid
7.0ms	18×	body	160	valid

simplify180.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize88.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

27.0ms	(* r (sin b))
59.0ms	(/ (* r (sin b)) (cos (+ a b)))
49.0ms	(cos (+ a b))

series407.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* r (sin b))
254.0ms	(/ (* r (sin b)) (cos (+ a b)))
56.0ms	(cos (+ a b))

simplify5.3s

Counts

59 → 59

Iterations

Iter	Nodes
done	5015
3	2732
2	632
1	214
0	95

prune956.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize118.0ms

Local error

Found 4 expressions with local error:

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

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 85

Calls

4 calls:

48.0ms	(* (cos a) (cos b))
27.0ms	(* r (sin b))
88.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
55.0ms	(* (sin a) (sin b))

series867.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos a) (cos b))
65.0ms	(* r (sin b))
619.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms	(* (sin a) (sin b))

simplify8.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
3	4692
2	1180
1	396
0	162

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize201.0ms

Local error

Found 4 expressions with local error:

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

rewrite404.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 109

Calls

4 calls:

36.0ms	(* (cos a) (cos b))
232.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
38.0ms	(* (sin a) (sin b))
91.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.4s

Counts

4 → 12

Calls

4 calls:

366.0ms	(* (cos a) (cos b))
630.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
81.0ms	(* (sin a) (sin b))
335.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.7s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	1513
1	466
0	192

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize120.0ms

Local error

Found 4 expressions with local error:

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

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `div-inv` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 96

Calls

4 calls:

68.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
39.0ms	(* (cos b) (cos a))
32.0ms	(/ (* (cos b) (cos a)) (sin b))
100.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series1.0s

Counts

4 → 12

Calls

4 calls:

230.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
75.0ms	(* (cos b) (cos a))
165.0ms	(/ (* (cos b) (cos a)) (sin b))
556.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify8.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5013
3	4629
2	1128
1	390
0	179

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes865.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	2918×	body	1280	valid
1.7s	1912×	body	640	valid
340.0ms	2095×	body	80	valid
314.0ms	705×	body	320	valid
92.0ms	370×	body	160	valid